Cremona's table of elliptic curves

1938 = 2 · 3 · 17 · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 17+ 19-	Signs for the Atkin-Lehner involutions
Class	1938d	Isogeny class
Conductor	1938	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5632	Modular degree for the optimal curve
Δ	2084975935488 = 222 · 34 · 17 · 192	Discriminant
Eigenvalues	2+ 3+  4  2  0 -2 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-9673,355525]	[a1,a2,a3,a4,a6]
j	100109991859083289/2084975935488	j-invariant
L	1.6514277632024	L(r)(E,1)/r!
Ω	0.82571388160121	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15504v1 62016z1 5814t1 48450by1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1938d1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	+	4	2	0	-2	+	-	6	0	2	4	-2	4	8	-10	4	-8	-4	14	-6	-6	12	-2	-2

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Quadratic twists for elliptic curve 1938d1

-4	8	-3	5	-7	17	-19
15504v1	62016z1	5814t1	48450by1	94962v1	32946m1	36822bb1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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